Maximization of Homogeneous Polynomials over the Simplex and the Sphere: Structure, Stability, and Generic Behavior

  • Faizan AhmedEmail author
  • Georg Still


The paper deals with the problem of maximizing a (nonconvex) homogeneous polynomial over the unit simplex. This program is directly related to the concept of evolutionarily stable strategies in biology. Optimality conditions are studied together with related stability properties. It is shown that generically any local maximizer is an evolutionarily stable strategy. We further extend these results to the case of polynomial optimization over the sphere.


Optimization over the simplex Homogeneous polynomials Evolutionarily stable strategies Stability of maximizers Genericity properties 

Mathematics Subject Classification

90C26 90C31 90C46 91A22 



The authors would like to thank the anonymous referees for many valuable comments and suggestions.


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Authors and Affiliations

  1. 1.Department of Applied Mathematics and StatisticsInstitute of Space TechnologyIslamabadPakistan
  2. 2.Department of MathematicsUniversity of TwenteEnschedeThe Netherlands

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